vrsyrotiuk@water.waterloo.edu (Violet Syrotiuk) (03/20/89)
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES
SCIENTIFIC COMPUTATION SEMINAR
- Thursday, March 23, 1989
Dr. Nicholas J. Higham*, of the Department of Computer
Science, Cornell University, will speak on ``Exploiting
Fast Matrix Multiplication Within the Level 3 BLAS''.
TIME: 1:30 PM
ROOM: DC 1304
ABSTRACT
The Level 3 BLAS (BLAS3) are a set of specifications of
Fortan 77 subprograms for carrying out matrix
multiplications and the solution of triangular systems
with multiple right-hand sides. They are intended to
provide efficient and portable building blocks for
linear algebra algorithms on high performance
computers. We describe algorithms for the BLAS3
operations that are asymptotically faster than the
conventional ones. These algorithms are based on
Strassen's method for fast matrix multiplication, which
is now recognized to be a practically useful technique
once matrix dimensions exceed about 100. We pay
particular attention to the numerical stability of
these ``fast BLAS3''. Error bounds are given and their
significance is explained and illustrated with the aid
of numerical experiments. Our conclusion is that the
fast BLAS3, although not as strongly stable as
conventional implementations, are stable enough to be
suitable for use in many applications.
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* On leave from the University of Manchester
--
Violet R. Syrotiuk | vrsyrotiuk@water.uucp
Computer Science Dept. | watmath!water!vrsyrotiuk
University of Waterloo | vrsyrotiuk@water.uwaterloo.ca
Waterloo, ON N2L 3G1 | vrsyrotiuk@water.waterloo.edu (or .cdn)